ALBANY – Mayor Bloomberg – who just took himself out of the presidential running – handed the state’s top Republican a $500,000 campaign contribution last month to keep open the option of running for governor in 2010, GOP sources said yesterday.

Bloomberg was openly encouraged to run by Senate Majority Leader Joseph Bruno (R-Rensselaer) during their meeting in City Hall Thursday, the day Hizzoner finally flatly declared that he would not try to run for president as an independent candidate, The Post has learned.

“Sen. Bruno did joke with the mayor, saying, ‘Now that you’ve taken yourself out of the race for president, you’re available to run for governor,’ ” recalled Bruno’s spokesman, John McArdle.

“It was done in a light way, but it is still the case that Senator Bruno strongly believes the mayor would be a tremendous candidate for governor, who would win.”

A Republican insider said the mayor was “seeking to keep all his options open, including the option of running for governor.”

“Where does Bloomberg go after he leaves being mayor, especially if his latest dance about running for vice president comes out in the same place as it did with his running for president?” said the GOP activist.

Bloomberg, who must leave office next year because of term limits, has repeatedly insisted that he’s not interested in running for governor, although Bruno – and other Republicans – have predicted he would run.

Such a contest would likely pit the billionaire Bloomberg against mega-million aire Democrat Gov. Spitzer, who is expected to seek re-election.

While Bloomberg and Spitzer have had generally cordial public relations, there is considerable tension and even dislike between them, political insiders say.

Since taking himself out of the prez stakes last week, Bloomberg has been touted by Deputy Mayor Kevin Sheekey as a poten tial vice-presidential running mate for Democrat Barack Obama, who phoned the mayor Friday.

Bloomberg’s huge contribution to Bruno’s Senate Republican Campaign Committee was disclosed by The New York Times yesterday in what appeared to be an effort to bolster the state’s hard- pressed GOP in the wake of a disastrous loss of a special Senate upstate election.

The Tuesday loss left Republicans with a mere single-vote majority in the Senate, the last bastion of GOP strength in the state.

Bloomberg’s contribution is similar in size to one made to the Senate GOP by the Democrat-turned- Republican-turned-independent two years ago.

Bloomberg has repeatedly praised Bruno and the Senate Republicans for what he says is their strong support of New York City.